Properties of Hausdorff Measures
Note that if d is a positive integer, the d dimensional Hausdorff measure of Rd is a rescaling of usual d-dimensional Lebesgue measure which is normalized so that the Lebesgue measure of the unit cube d is 1. In fact, for any Borel set E,
where αd is the volume of the unit d-ball; it can be expressed using Euler's gamma function
Remark. Some authors adopt a definition of Hausdorff measure slightly different from the one chosen here, the difference being that it is normalized in such a way that Hausdorff d-dimensional measure in the case of Euclidean space coincides exactly with Lebesgue measure.
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